Using Lagrangians to solve statics problems for compound shapes

[least_action]

Is it possible to do statics using lagrangians? (specifically building up a compound shape like a bridge from constrained point masses). Where could I see an example of this?

 

[fobos3]

Is it possible to do statics using lagrangians? (specifically building up a compound shape like a bridge from constrained point masses). Where could I see an example of this?

Yes, just put the Lagrangian equal to the potential energy. However I think you will find that, if you have an equilibrium the potential energy is at minimum more useful. For example consider the cantenary.

$$V=\int_C my\,ds$$

Now if you use Lagrangian mechanics you would be minimising $$\iint_C my\,ds\,dt$$ instead of $$\int_C my\,ds$$

 

[least_action]

Yes, just put the Lagrangian equal to the potential energy. However I think you will find that, if you have an equilibrium the potential energy is at minimum more useful. For example consider the cantenary.

$$V=\int_C my\,ds$$

Now if you use Lagrangian mechanics you would be minimising $$\iint_C my\,ds\,dt$$ instead of $$\int_C my\,ds$$

Thank you!